(a) The speed between t = 5 and t = 10 is calculated using the formula for speed, which is the change in displacement over time. The displacement changes from 50 m to 150 m over 5 seconds, so:

\(\text{Speed} = \frac{150 - 50}{10 - 5} = \frac{100}{5} = 20 \text{ ms}^{-1}\)

(b) To find the acceleration between t = 0 and t = 5, we use the equation of motion \(v = u + at\). The initial velocity \(u = 0\) (since the particle starts from rest), and the final velocity \(v = 20 \text{ ms}^{-1}\) at t = 5:

\(20 = 0 + a \times 5\)

Solving for \(a\):

\(a = \frac{20}{5} = 4 \text{ ms}^{-2}\)

(c) The average speed is calculated by dividing the total distance traveled by the total time taken. The particle travels 50 m to P, 100 m to Q, 50 m to R, and 200 m back to O:

\(\text{Total distance} = 50 + 100 + 50 + 200 = 400 \text{ m}\)

\(\text{Average speed} = \frac{400}{20} = 20 \text{ ms}^{-1}\)